diff --git a/python/gtsam/tests/test_ShonanAveraging.py b/python/gtsam/tests/test_ShonanAveraging.py
new file mode 100644
index 000000000..4c423574d
--- /dev/null
+++ b/python/gtsam/tests/test_ShonanAveraging.py
@@ -0,0 +1,139 @@
+"""
+GTSAM Copyright 2010-2019, Georgia Tech Research Corporation,
+Atlanta, Georgia 30332-0415
+All Rights Reserved
+
+See LICENSE for the license information
+
+Unit tests for Shonan Rotation Averaging.
+Author: Frank Dellaert
+"""
+# pylint: disable=invalid-name, no-name-in-module, no-member
+
+import unittest
+
+import gtsam
+from gtsam import ShonanAveraging3, ShonanAveragingParameters3
+from gtsam.utils.test_case import GtsamTestCase
+
+DEFAULT_PARAMS = ShonanAveragingParameters3(
+    gtsam.LevenbergMarquardtParams.CeresDefaults())
+
+
+def fromExampleName(name: str, parameters=DEFAULT_PARAMS):
+    g2oFile = gtsam.findExampleDataFile(name)
+    return ShonanAveraging3(g2oFile, parameters)
+
+
+class TestShonanAveraging(GtsamTestCase):
+    """Tests for Shonan Rotation Averaging."""
+
+    def setUp(self):
+        """Set up common variables."""
+        self.shonan = fromExampleName("toyExample.g2o")
+
+    def test_checkConstructor(self):
+        self.assertEqual(5, self.shonan.nrUnknowns())
+
+        D = self.shonan.denseD()
+        self.assertEqual((15, 15), D.shape)
+
+        Q = self.shonan.denseQ()
+        self.assertEqual((15, 15), Q.shape)
+
+        L = self.shonan.denseL()
+        self.assertEqual((15, 15), L.shape)
+
+    def test_buildGraphAt(self):
+        graph = self.shonan.buildGraphAt(5)
+        self.assertEqual(7, graph.size())
+
+    def test_checkOptimality(self):
+        random = self.shonan.initializeRandomlyAt(4)
+        lambdaMin = self.shonan.computeMinEigenValue(random)
+        self.assertAlmostEqual(-414.87376657555996,
+                               lambdaMin, places=3)  # Regression test
+        self.assertFalse(self.shonan.checkOptimality(random))
+
+    def test_tryOptimizingAt3(self):
+        initial = self.shonan.initializeRandomlyAt(3)
+        self.assertFalse(self.shonan.checkOptimality(initial))
+        result = self.shonan.tryOptimizingAt(3, initial)
+        self.assertTrue(self.shonan.checkOptimality(result))
+        lambdaMin = self.shonan.computeMinEigenValue(result)
+        self.assertAlmostEqual(-5.427688831332745e-07,
+                               lambdaMin, places=3)  # Regression test
+        self.assertAlmostEqual(0, self.shonan.costAt(3, result), places=3)
+        SO3Values = self.shonan.roundSolution(result)
+        self.assertAlmostEqual(0, self.shonan.cost(SO3Values), places=3)
+
+    def test_tryOptimizingAt4(self):
+        random = self.shonan.initializeRandomlyAt(4)
+        result = self.shonan.tryOptimizingAt(4, random)
+        self.assertTrue(self.shonan.checkOptimality(result))
+        self.assertAlmostEqual(0, self.shonan.costAt(4, result), places=2)
+        lambdaMin = self.shonan.computeMinEigenValue(result)
+        self.assertAlmostEqual(-5.427688831332745e-07,
+                               lambdaMin, places=3)  # Regression test
+        SO3Values = self.shonan.roundSolution(result)
+        self.assertAlmostEqual(0, self.shonan.cost(SO3Values), places=3)
+
+    def test_initializeWithDescent(self):
+        random = self.shonan.initializeRandomlyAt(3)
+        Qstar3 = self.shonan.tryOptimizingAt(3, random)
+        lambdaMin, minEigenVector = self.shonan.computeMinEigenVector(Qstar3)
+        initialQ4 = self.shonan.initializeWithDescent(
+            4, Qstar3, minEigenVector, lambdaMin)
+        self.assertAlmostEqual(5, initialQ4.size())
+
+    def test_run(self):
+        initial = self.shonan.initializeRandomly()
+        result, lambdaMin = self.shonan.run(initial, 5, 10)
+        self.assertAlmostEqual(0, self.shonan.cost(result), places=2)
+        self.assertAlmostEqual(-5.427688831332745e-07,
+                               lambdaMin, places=3)  # Regression test
+
+    def test_runKlausKarcher(self):
+        # Load 2D toy example
+        lmParams = gtsam.LevenbergMarquardtParams.CeresDefaults()
+        # lmParams.setVerbosityLM("SUMMARY")
+        g2oFile = gtsam.findExampleDataFile("noisyToyGraph.txt")
+        parameters = gtsam.ShonanAveragingParameters2(lmParams)
+        shonan = gtsam.ShonanAveraging2(g2oFile, parameters)
+        self.assertAlmostEqual(4, shonan.nrUnknowns())
+
+        # Check graph building
+        graph = shonan.buildGraphAt(2)
+        self.assertAlmostEqual(6, graph.size())
+        initial = shonan.initializeRandomly()
+        result, lambdaMin = shonan.run(initial, 2, 10)
+        self.assertAlmostEqual(0.0008211, shonan.cost(result), places=5)
+        self.assertAlmostEqual(0, lambdaMin, places=9)  # certificate!
+
+    # Test alpha/beta/gamma prior weighting.
+    def test_PriorWeights(self):
+        lmParams = gtsam.LevenbergMarquardtParams.CeresDefaults()
+        params = ShonanAveragingParameters3(lmParams)
+        self.assertAlmostEqual(0, params.getAnchorWeight(), 1e-9)
+        self.assertAlmostEqual(1, params.getKarcherWeight(), 1e-9)
+        self.assertAlmostEqual(0, params.getGaugesWeight(), 1e-9)
+        alpha, beta, gamma = 100.0, 200.0, 300.0
+        params.setAnchorWeight(alpha)
+        params.setKarcherWeight(beta)
+        params.setGaugesWeight(gamma)
+        self.assertAlmostEqual(alpha, params.getAnchorWeight(), 1e-9)
+        self.assertAlmostEqual(beta, params.getKarcherWeight(), 1e-9)
+        self.assertAlmostEqual(gamma, params.getGaugesWeight(), 1e-9)
+        params.setKarcherWeight(0)
+        shonan = fromExampleName("Klaus3.g2o", params)
+
+        initial = gtsam.Values()
+        for i in range(3):
+            initial.insert(i, gtsam.Rot3())
+        self.assertAlmostEqual(3.0756, shonan.cost(initial), places=3)
+        result, _lambdaMin = shonan.run(initial, 3, 3)
+        self.assertAlmostEqual(0.0015, shonan.cost(result), places=3)
+
+
+if __name__ == '__main__':
+    unittest.main()